On the Eneström-Kakeya theorem for quaternionic polynomial

Abstract

The main purpose of this paper is to extend various results of Enestr?m-Kakeya type from the complex to quaternionic setting by virtue of a maximum modulus theorem and the structure of the zero sets in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our findings generalise several newly proven conclusions concerning the distribution of zeros of a quaternionic polynomial.